Another national group with a local chapter, Stand for Children, has just begun the formal process of vetting candidates. And several wealthy benefactors of the movement tell WBUR they plan to spend in the race.

At least one, venture capitalist and education activist Chris Gabrieli, has held an event raising money for Connolly’s campaign.

But education reform advocates have not yet coalesced around a single candidate. State Rep. Martin J. Walsh, who helped start the Neighborhood House Charter School in Dorchester, and Shawmut Design and Construction executive Bill Walczak, who founded the Codman Academy Charter Public School in Dorchester, have drawn interest from the outset.

Advocates add that Suffolk County District Attorney Daniel Conley has impressed on the campaign trail.

Backing a candidate at this early stage in the race comes with some risk for DFER. A gaffe or embarrassing story in the media could derail Connolly’s candidacy. But the group is betting it can have a bigger impact on the campaign if it starts canvassing now.

If Connolly fails to survive a preliminary election in September, which will narrow the 12-member field to two, DFER will only stay in the race if there is a substantial difference on education reform between the remaining candidates.

The market-based reform movement — charter schools, standardized tests, data-driven evaluation of teachers — has become a potent force in recent decades, embraced by figures from New York Mayor Michael Bloomberg to President Barack Obama.

But it has not yet claimed success in a large American city.

Local supporters and national observers are emboldened by the success of Boston’s charter schools, though. And they believe the city, with its network of academic and non-profit partners and relatively small number of students, could be the first to close the achievement gap separating white and Asian students from blacks and Latinos.

Election of a supportive mayor, reformers say, is critical to that effort.

But critics like Richard Stutman, president of the Boston Teachers Union, argue that DFER — launched by a number of prominent hedge fund managers — is engaged in a business-backed assault on public education.

“Just because someone puts the word ‘Democrat’ in front of their name doesn’t make them a Democrat,” he said.

Stutman, who has clashed publicly with Connolly, said the union will probably endorse a mayoral candidate of its own in early September.

Connolly has made education the signature issue of his City Council career.

In 2011, he made a splash when he uncovered expired frozen food in school cafeterias. And he was the lone vote against the most recent teacher contract, objecting to its failure to extend the school day.

He has also embraced the central components of education reform agenda. He wants the state to lift a cap on charter schools. And he has called for a decentralization of the school system, with authority shifting from the district headquarters on Court Street to principals.

Reformers believe that a principal with the power to hire and fire teachers and dictate the school schedule is the most important change agent in public education.

DFER’s Massachusetts chapter has hired veteran Democratic political operative Marty Walsh, who served as a consultant on U.S. Rep. Joseph Kennedy III’s campaign and ran U.S. Sen. Elizabeth Warren’s South Coast election operation last fall, to oversee its canvassing effort.

Other staff include field organizers from U.S. Rep. Edward Markey’s successful bid for a U.S. Senate seat this spring.

Kerr said the group has no particular dollar figure in mind for its independent expenditure campaign. But with no immediate plans for television or radio advertising, he said, the group can run a relatively low-cost operation.

The group spent about $12,000 backing state Rep. Nick Collins’ unsuccessful bid for a state senate seat in a special election this spring.

As it weighed its endorsement, DFER commissioned a one-question poll in mid-June — asking almost 2200 voters whom they would support for mayor if the election were held today.

Fully 71 percent of voters were undecided. But Connolly placed first among the rest, with 6.98 percent of the vote. Conley was second with 4.56 percent. Walsh was third at 3.47 percent.

Connolly, who holds an at-large City Council seat, also appears to have the broadest support across the city at this early stage. He claims at least 5 percent of the vote in 13 of the city’s 22 wards, with the strongest support in Ward 2, in Charlestown, and Ward 20, which includes West Roxbury, where he lives, and parts of Roslindale.

Walsh, who finished second by that measure, had at least 5 percent of the vote in six wards.

New York City-based Democrats for Education Reform, launched in 2007, has chapters in 13 states across the country.

Run by Joe Williams, a former reporter at the New York Daily News and Milwaukee Journal Sentinel, the group is active in both electoral politics and issue advocacy.

DFER has supported candidates for the New Jersey state legislature and the Denver school board. Last year, it backed Chicago Mayor Rahm Emanuel in his high-profile showdown with the city’s teachers union.

The organization worked closely with Stand for Children on that effort, as it has on others.

Stand, founded in 1996 by Jonah Edelman, the son of prominent civil rights activist, has developed a reputation for a hard-nosed, effective politics.

In 2011, Edelman told a crowd at the Aspen Ideas Festival that Illinois teachers unions were concerned about legislation the group championed earlier that year because Stand could “jam this proposal down their throats.”

Edelman later apologized for the comment.

Last year, Stand’s 10-year old Massachusetts chapter made waves when it forced teachers to give up certain seniority rights after threatening to put the matter on the ballot.

Sam Castañeda Holdren, a spokesman for the Massachusetts chapter, said Stand is sending questionnaires to all the mayoral and City Council candidates this week.

A committee of staffers and members will review the responses and invite viable candidates of interest for interviews. The group will then decide whether to endorse any candidates in the City Council or mayoral races.